# Probability, Confidence Interval & Hypothesis Testing

See attached file for 3 problems: Tesla Motors, PC manufacturer and large insurance company claims

4. Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla's requirement is that 95% of the axles are 100 cm ± 2 cm. The following data is MegaStat output from a test run from Chris Cross Manufacturing. Should Tesla select them as a vendor? Explain your answer.

Descriptive statistics

count 16

mean 99.938

sample variance 2.313

sample standard deviation 1.521

minimum 97

maximum 102.9

range 5.9

population variance 2.169

population standard deviation 1.473

standard error of the mean 0.380

tolerance interval 95.45% lower 96.896

tolerance interval 95.45% upper 102.979

half-width 3.042

1st quartile 98.900

median 99.850

3rd quartile 100.475

interquartile range 1.575

mode 98.900

5. A PC manufacturer claims that no more than 5% of their machines are defective. In a random sample of 100 machines, it is found that 8.5% are defective. The manufacturer claims this is a fluke of the sample. At a .02 level of significance, test the manufacture's claim, and explain your answer..

MegaStat Output

Hypothesis test for proportion vs. hypothesized value

Observed Hypothesized

0.085 0.05 p (as decimal)

9/100 5/100 p (as fraction)

8.5 5.0 X

100 100 n

0.0218 std. error

1.61 Z

.0541 p-value (one-tailed, upper)

6. The following table gives the number of claims at a large insurance company by kind and geographical region.

East South

Midwest

West

Totals

Hospitalization

102

98

39

62

301

Physician's Visit

263

514

120

351

1248

Outpatient Treatment

100

226

65

99

490

Totals

465

838

224

512

2039

(A) Referring to the above table, if a bill is chosen at random, what is the probability that it is either from the East or from the West?

(B) Referring to the above table, given that the bill is from the Midwest, what is the probability that it is for a Physician's Visit?

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval, hypothesis testing and probability. Formula for the calculation and Interpretations of the results are also included.